A118176 a(1) = 1. a(n) is the number of earlier terms of the sequence which have a different number of divisors than n.

1, 1, 2, 3, 2, 5, 2, 7, 8, 8, 4, 11, 5, 11, 12, 15, 7, 16, 8, 18, 16, 17, 11, 23, 23, 21, 21, 25, 14, 29, 15, 29, 24, 25, 26, 35, 20, 27, 27, 38, 24, 39, 26, 40, 41, 30, 29, 47, 45, 45, 35, 46, 33, 49, 36, 51, 37, 38, 38, 59, 39, 39, 57, 63, 40, 60, 45, 60, 44, 64, 49, 69, 51, 47

Offset

1,3

Comments

A118177(n) is the number of divisors of a(n).

Links

Michel Marcus, Table of n, a(n) for n = 1..10000 (terms 1 to 100 from M. F. Hasler)

Example

11 has 2 divisors. So a(11) = the number of terms among the first 10 terms of the sequence which do not have 2 divisors. Only the four terms a(1) = 1, a(2) = 1, a(9) = 8 and a(10) = 8 each do not have 2 divisors. So a(11) = 4.

Maple

a:=proc(n)option remember; if n=1 then 1 else nops( subs( numtheory[tau](n)=NULL, [ 'numtheory[tau](a(i))', $i=1..n-1 ] )) fi end; # M. F. Hasler, Nov 06 2006

Mathematica

a[n_] := a[n] = If[n == 1, 1, Count[Array[a, n-1], t_ /; DivisorSigma[0, n] != DivisorSigma[0, t]]];
Array[a, 100] (* Jean-François Alcover, Oct 01 2020 *)

Prog

(PARI) lista(nn) = {my(va = vector(nn), vd = vector(nn)); va[1] = 1; vd[1] = numdiv(1); for (n=2, nn, va[n] = sum(k=1, n-1, vd[k] != numdiv(n)); vd[n] = numdiv(va[n]); ); va; } \\ Michel Marcus, Oct 01 2020

Crossrefs

Cf. A000005, A118177.

Sequence in context: A346703 A271774 A331602 * A005731 A132962 A046145

Adjacent sequences: A118173 A118174 A118175 * A118177 A118178 A118179

Keyword

nonn

Author

Leroy Quet, Apr 13 2006

Extensions

More terms from M. F. Hasler, Nov 06 2006

Status

approved